Argand diagram

Hi I would really appreciate your time for this, I would really like to know if my interpretations on the argand diagram are right!

Where w and z are complex numbers,
Let arg(z)-arg(w) = 90 degrees where arg(z) is represented by theta and arg(w) is represented by alpha.

I drew two interpretations of arg(z)-arg(w) = 90 degrees on the argand diagram, am I right in the images below?

I am not sure if I am right as they both yield different equations like one diagram shows theta-alpha to get 90 degrees whilst the other alpha-theta to get 90 degrees..I was wondering if this is the reason why you would insert a modulus, |alpha-theta| = 90 degrees..can someone help me out?

Thank you so so so so so so much, you dont know how much this means to me!